Question

A rectangular container, whose base is a square of side 5 cm, stands on a horizontal table, and holds water upto 1 cm from the top. When a cube is placed in the water it is completely submerged, the water rises to the top and 2 cubic cm of water overflows. Calculate the volume of the cube and also the length of its edge.

Answer 1

$\text{Base of the container}=5cm\times 5cm$

$\text{After placing a cube in it, the water rises to the top (i.e. by 1 cm) and 2 cubic cm of water overflows.}$

$\left(i\right)\therefore \text{Volume of water}=5\times 5\times 1+2$$=25+2=27c{m}^3$

$\therefore \text{Volume of cube}=27c{m}^3$

$\left(ii\right)\text{Then edge of the cube}=\sqrt[3]{327}=3cm$